Question

in westminster, the library is due south of the courthouse and due west of the community swimming pool. if the distance between the library and the courthouse is 12 kilometers and the distance between the courthouse and the city pool is 15 kilometers, how far is the library from the community pool? kilometers

Explanation:

Step1: Recognize right - triangle situation

The positions of the library, courthouse, and community pool form a right - triangle, where the distance between the courthouse and the community pool is the hypotenuse ($c = 15$ km) and the distance between the library and the courthouse is one leg ($a = 12$ km). We need to find the other leg ($b$).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We can rewrite it to solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 12$ and $c = 15$ into the formula:
$b=\sqrt{15^{2}-12^{2}}=\sqrt{(15 + 12)(15 - 12)}=\sqrt{27\times3}=\sqrt{81}$.

Step3: Calculate the value of $b$

$\sqrt{81}=9$.

Answer:

9